I agree with you and a lot of others that the thought of overly influencing politics 'back in the UK' with your vote is an uncomfortable one. But this isn't an election that's going to be primarily about domestic policy, in which you'll be treading on toes and out of the loop.
You won't be someone making their voting based on free travel for OAPS/refunding middle class graduates loans/booting out foreign people/tax breaks for small businesses. You'd be someone voting on, among other things, what your citizenship is going to mean. What your passport is going to do. How you will be treated on travel outside of your country of residence and the UK.
You'd also, if voting for the Labour candidate to ward off the second placed conservative threat, be voting in (on balance) the best interests of residents of the UK. As a remainer who is familiar with the economic analysis of what brexit would cost. Last but not least, you have a vote legally, it's your entitlement - it's not like you're pulling the wool over someones eyes by registering a fake address or something.
Genuinely the bigger moral dilemma in my view is voting for a party that's got institutional problems with anti-semitism, a culture of bullying and poor workplace mental health, with a weirdo anti western fetishism marriage of anti western regressive left OAPs and islamist fascists. It's a dilemma I share, having just moved into Keir Startmers seat. On the one hand I think his passivity has seen him be the leaderships useful idiot, legitimising their crap brexit position up until this summer. On the other I know that he's someone on the inside of the party who is trying to achieve what I want.